(57) Rolling mill work and back-up rolls comprising an arbor (35) with a sleeve (36) shrunk thereon have circum­ferential grooves (37, 38, 39) formed in the external surface of the arbor (35), through which heating or cooling liquid is supplied from external sources so as to expand or contract the sleeve (36) and change the roll crown and contour. The fins (53), or material between grooves, may have higher heat conductivity than the material of the arbor (35) and sleeve (36), and are proportioned to transmit roll­ing forces without reducing roll stiffness. A liquid supply system provides liquids of different temperatures to selected sections of the grooves along the roll work­ing surface; and strip of different widths but of uniform gauge across the strip is rolled by suitably adjusting the temperatures of the hot and cold liquids so supplied.